1. Chapter 5 Time Value of Money

2. Learning Objectives Describe the basic mechanics of the time value of money Perform calculations related to discounting and compounding. 5-1

3. Terms Compounding Discounting Compounding or Discounting Rate Future Value Present Value Lump Sum Annuity 5-2

4. Calculations Future Value of a Lump Sum Present Value of a Lump Sum Future Value of an Annuity Sinking Fund Future Value of an Annuity Due Present Value of an Annuity Mortgage Constant Present Value of an Annuity Due 5-3

5. Future Value of a Lump Sum May B. Wiser invests 10,000 today earning 5%, compounded annually. What is the value of the investment in 5 years? FV 5 = 10,000(1.05) 5 = $12,762.82 5-4

6. Present Value of a Lump Sum May B. Wiser can make an investment that will pay $1,500 at the end of year three. With a discount rate of 6%, what is the present value of the investment? PV = 1500/(1.06) 3 = $1259.43 5-5

7. Future Value of an Annuity May B. Wiser will receive 1,000 at the end of each year for the next five years. If her investment rate is 6%, what is the future value of this annuity? FVANN 5 = 1,000[((1.06) 5 -1)/.06] = $5,637.09 5-6

8. Sinking Fund If May B. Wiser needs $15,000 at the end of the five years to make a down payment on her dream home, how much must she save each year if she earns 8% on investment funds? Pmt = 15,000[0.8/((1.08) 5 -1)] = $2,556.85 5-8

9. Future Value of Annuity Due May B. Wiser will receive 1,000 at the beginning of each year for the next five years. If her investment rate is 6%, what is the future value of this annuity due? FVAD 5 = 1,000[((1.06) 5 -1)/0.6] (1.06) = $5,9750.32 5-9

10. Present Value of an Annuity May B. Wiser will receive $1,000 at the end of each year for the next five years. What is the present value of this annuity if the discount rate is 6%? PVANN 5 = 1,000[((1.06) 5 -1)/((0.6)(1.06) 5 ) = $4,2120.36 5-10

11. Mortgage Constant May B. Wiser takes a fixed-rate mortgage for $100,000 at 8% for thirty years to buy her dream home. What is her monthly payment? Pmt = 100,000[ ((.08/12)(1+.08/12) 360 )/((1+.08) 360 -1)] = $733.76 5-11

12. Present Value of an Annuity Due May B. Wiser will receive $1,000 at the beginning of each year for the next five years. What is the present value of this annuity due if the discount rate is 6%? PVAD 5 = 1,000[((1.06) 5 -1)/((.06)(1.06) 5 )](1.06)= $4,465.10 5-12